Abstract
For an odd integer n ≥ 3, an odd prime p ≡ 3(mod4) and \({d=\frac{p^n+1}{p+1}-\frac{p^n-1}{2}}\), the value distribution of the exponential sum \({\sum\limits_{x\in \mathbb{F}_{p^n}^{\,*}}\omega^{Tr^n_1(x-\gamma x^{d})}\,(\gamma\in \mathbb{F}_{p^n}^{*})}\) is completely determined in this paper, where ω is a primitive complex p-th root of unity. This improves the results of Müller (1999) and Hu et al. (2001) about the crosscorrelation of sequences with the decimation factor d.
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This work was partially supported by the National Natural Science Foundation of China under Grants 60973130, 60773134, 10990011, and National Basic Resarch (973) Program of China (2007CB311201).
The work of X. Zeng was also supported by the Natural Science Foundation for Excellent Youth Scholars of Hubei Province of China (2009CDA147).
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Xia, Y., Zeng, X. & Hu, L. Further crosscorrelation properties of sequences with the decimation factor \({d=\frac{p^n+1}{p+1}-\frac{p^n-1}{2}}\) . AAECC 21, 329–342 (2010). https://doi.org/10.1007/s00200-010-0128-y
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DOI: https://doi.org/10.1007/s00200-010-0128-y